The Bruins are on the verge of the Stanley Cup finals — provided Lightning doesn’t strike twice.

It was the Bruins who struck decisively last night, overcoming an early one-goal deficit for a critical 3-1 victory over the Lightning in Game 5 of the Eastern Conference finals at the Garden.

Leading 3-2 in the best-of-seven series, the B’s are now one victory away from reaching the Stanley Cup finals for the first time since 1990.

Game 6 is tomorrow night in Tampa. In their history, the Bruins are 17-4 in Game 6’s after winning Game 5 of a 2-2 series.

Brad Marchand tallied the game-winner late in the second period, and Tim Thomas made 33 saves. Rich Peverley added an empty-net goal with 12.1 seconds left to seal it, just before a brawl ensued after the final horn, adding an extra dimension to tomorrow’s Game 6.

Despite being outshot 23-12 through two periods, the Bruins led when it mattered, taking a 2-1 lead into the second intermission on the strength of two second-period goals.

The latter was among the prettiest of the postseason, with Patrice Bergeron recovering a loose puck near the corner to the left of Lightning goalie Mike Smith and slipping a pinpoint pass just beyond two defenders to a cutting Marchand.

The Lightning needed just 69 seconds in the first period to take a 1-0 lead, with Steven Stamkos feeding Simon Gagne on a 2-on-1 breakaway after David Krejci lost the puck at the top of the Tampa Bay zone.

Nathan Horton pulled the Bruins into a tie 4:24 into the second period, taking a perfect pass from Milan Lucic and beating Smith.